R commands and output: ## Read data and compute summary statistics. y <- scan("ZARR13.DAT",skip=25) ybar = mean(y) std = sd(y) n = length(y) stderr = std/sqrt(n) Statistics = c(round(length(y),0),round(ybar,5),round(std,5), round(stderr,5)) names(Statistics)= c("Number of Observations ", "Mean", "Std. Dev.", "Std. Dev. of Mean") ## Compute confidence intervals. alpha = c(.5, .25, .10, .05, .01, .001, .0001, .00001) Conf.Level = 100*(1-alpha) Tvalue = qt(1-alpha/2,df=n-1) Halfwidth = Tvalue*stderr Lower = ybar - Tvalue*stderr Upper = ybar + Tvalue*stderr ci = round(cbind(alpha, Conf.Level, Tvalue, Halfwidth, Lower, Upper),6) ## Print results. data.frame(Statistics) > Statistics > Number of Observations 195.00000 > Mean 9.26146 > Std. Dev. 0.02279 > Std. Dev. of Mean 0.00163 data.frame(ci) > alpha Conf.Level Tvalue Halfwidth Lower Upper > 1 0.50000 50.000 0.675756 0.001103 9.260358 9.262564 > 2 0.25000 75.000 1.153804 0.001883 9.259578 9.263344 > 3 0.10000 90.000 1.652746 0.002697 9.258764 9.264158 > 4 0.05000 95.000 1.972268 0.003219 9.258242 9.264679 > 5 0.01000 99.000 2.601409 0.004245 9.257215 9.265706 > 6 0.00100 99.900 3.341382 0.005453 9.256008 9.266914 > 7 0.00010 99.990 3.973014 0.006484 9.254977 9.267944 > 8 0.00001 99.999 4.536689 0.007404 9.254057 9.268864 ## Perform one sample t-test. z = t.test(y,alternative="two.sided",mu=5) > One Sample t-test > data: y > t = 2611.286, df = 194, p-value < 2.2e-16 > alternative hypothesis: true mean is not equal to 5 > 95 percent confidence interval: > 9.258242 9.264679 > sample estimates: > mean of x > 9.26146